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Progress:\newlineMatch the polynomial on the left with the simplified polynomial on the right.\newlineQuotation ID: 11\newline{(4x2y5xy2+2x2y2+2xy)+(2x2y+4xy+2xy22x2y2)6x2y3x2y2+2xy22y 6x2y2+4x2y2xy2+2x2y 18x3y2+9x2y312x3y3+6xy23xy {6x2y2+3x2y7xy2xy2+2y 6x2y3xy2+6xy\left\{\begin{array}{l} \left(4x^{2}y-5xy^{2}+2x^{2}y^{2}+2xy\right)+\left(2x^{2}y+4xy+2xy^{2}-2x^{2}y^{2}\right) - 6x^{2}y-3x^{2}y^{2}+2xy^{2}-2y \ -6x^{2}y^{2}+4x^{2}y-2xy^{2}+2x-2y \ \frac{18x^{3}y^{2}+9x^{2}y^{3}-12x^{3}y^{3}+6xy^{2}}{3xy} \ \left\{\begin{array}{l} 6x^{2}y^{2}+3x^{2}y-7xy-2xy^{2}+2y \ 6x^{2}y-3xy^{2}+6xy \end{array}\right. \end{array}\right.\newlineClear

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Q. Progress:\newlineMatch the polynomial on the left with the simplified polynomial on the right.\newlineQuotation ID: 11\newline{(4x2y5xy2+2x2y2+2xy)+(2x2y+4xy+2xy22x2y2)6x2y3x2y2+2xy22y 6x2y2+4x2y2xy2+2x2y 18x3y2+9x2y312x3y3+6xy23xy {6x2y2+3x2y7xy2xy2+2y 6x2y3xy2+6xy\left\{\begin{array}{l} \left(4x^{2}y-5xy^{2}+2x^{2}y^{2}+2xy\right)+\left(2x^{2}y+4xy+2xy^{2}-2x^{2}y^{2}\right) - 6x^{2}y-3x^{2}y^{2}+2xy^{2}-2y \ -6x^{2}y^{2}+4x^{2}y-2xy^{2}+2x-2y \ \frac{18x^{3}y^{2}+9x^{2}y^{3}-12x^{3}y^{3}+6xy^{2}}{3xy} \ \left\{\begin{array}{l} 6x^{2}y^{2}+3x^{2}y-7xy-2xy^{2}+2y \ 6x^{2}y-3xy^{2}+6xy \end{array}\right. \end{array}\right.\newlineClear
  1. Combine Like Terms: First, let's simplify the polynomial expression on the left by combining like terms.\newlineWe have:\newline(4x2y5xy2+2x2y2+2xy)+(2x2y+4xy+2xy22x2y2)6x2y3x2y2+2xy22y(4x^2y - 5xy^2 + 2x^2y^2 + 2xy) + (2x^2y + 4xy + 2xy^2 - 2x^2y^2) - 6x^2y - 3x^2y^2 + 2xy^2 - 2y\newlineCombine like terms:\newline(4x2y+2x2y6x2y)+(5xy2+2xy2+2xy2)+(2x2y22x2y23x2y2)+(2xy+4xy)2y(4x^2y + 2x^2y - 6x^2y) + (-5xy^2 + 2xy^2 + 2xy^2) + (2x^2y^2 - 2x^2y^2 - 3x^2y^2) + (2xy + 4xy) - 2y\newlineNow, simplify each group:\newline(4x2y+2x2y6x2y)=0(4x^2y + 2x^2y - 6x^2y) = 0\newline(5xy2+2xy2+2xy2)=1xy2(-5xy^2 + 2xy^2 + 2xy^2) = -1xy^2\newline(2x2y22x2y23x2y2)=3x2y2(2x^2y^2 - 2x^2y^2 - 3x^2y^2) = -3x^2y^2\newline(2xy+4xy)=6xy(2xy + 4xy) = 6xy\newlineAnd we have 2y-2y as it is.\newlineSo, the simplified polynomial is:\newline01xy23x2y2+6xy2y0 - 1xy^2 - 3x^2y^2 + 6xy - 2y\newlineWhich simplifies further to:\newlinexy23x2y2+6xy2y-xy^2 - 3x^2y^2 + 6xy - 2y

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